Papers with an overall presentation of the TBM.

Papers on the TBM.

Papers on applications of the TBM.

Papers on the TBM and Non-Monotonic Reasoning.

Papers on the TBM and decision.

Papers on Belief Decision Trees.

Papers on the FMT (Fast Möbius Transform).

Papers comparing the TBM with other theories.

Papers on the representation on uncertainty.

Papers on fuzzy sets theory.

Note: I did as well as possible in creating the .ps and .pdf files, but errors might have occurred. So if you find some errors or some difficulties in loading the .ps or the .pdf version, please send me an email at psmets@ulb.ac.be. Thanks.

Smets Ph. Magrez P. (1987) La représentation de la croyance.
Revue de l'Intelligence Artificielle, 1 (1987) 31-46.

Smets Ph. (1988) Belief Functions.
Non Standard Logics for Automated Reasoning. Smets Ph., Mamdani A., Dubois D. and Prade H. (Editors) Academic Press, London. 253-286.

Smets Ph. and Kennes R. (1994) The transferable belief model.
Artificial Intelligence 66 (1994) 191-234.
TBM-AIJ.ps
TBM-AIJ.pdf

Smets Ph. and Kruse R. (1997) The Transferable Belief Model for Belief Representation.
Motro A. and Smets Ph. (eds.) (1993) Uncertainty Management in information systems: from needs to solutions. Kluwer, Boston, (1997) 343-368.
TBM-InformSystem.ps
TBM-InformSystem.pdf

Smets Ph. (1998) The Transferable Belief Model for Quantified Belief Representation.
Handbook of Defeasible Reasoning and Uncertainty Management Systems. Gabbay D. and Smets Ph. (Series Eds). Ph. Smets (Vol. eds.), Vol. 1 : Quantified Representation of Uncertainty & Imprecision, Kluwer, Doordrecht (1998) 267-301.
TBM-hdbk.ps
TBM-hdbk.pdf

Smets Ph. (2000) Data Fusion in the Transferable Belief Model.
Proc. 3rd Intern. Conf. Inforation Fusion, Paris, France (2000) PS21-33.
An invited talk of data fusion handled with the TBM, with a view on applications.
Data-Fusion.ps
Data-Fusion.pdf

Papers on the TBM.  

Smets Ph. (1984) Combination of Non Distinct Evidences.
Proceedings of the 1984 American Control Conference, (1984) 554-555.

Smets Ph. (1990) The Combination of Evidence in the Transferable Belief Model.
IEEE Trans. PAMI 12 (1990) 447-458.
An axiomatic derivation of the Dempster's rule of combination.
Axioms for Dempster Combination.ps
Axioms for Dempster Combination.pdf

Smets Ph.(1991) About Updating.
Proceedings of the 7th conference on Uncertainty in Artificial Intelligence, D'ambrosio, B. and Smets, Ph. and and, Bonissone P. P. (eds), Morgan Kaufmann Publ., San Mateo, California. (1991) 378-385.
A comparison through an example of the many updating rules one can observe with random set observations.
About Updating.ps
About Updating.pdf

Klawonn F. and Smets Ph. (1992) The Dynamic of Belief in the Transferable Belief Model and Specialization-Generalization Matrices.
Proceedings of the 8th Conference on Uncertainty in Artificial Intelligence. Dubois D., Wellman M.P., D’Ambrosio B. and Smets Ph. (eds). Morgan Kaufmann Publ., San Mateo, California. (1992) 130-137.
How to justify Dempster’s rule of combination as the least committed commutative specialization.
Specialization.ps
Specialization.pdf

Smets Ph. (1992) The Concept of Distinct Evidence.
Proceedings of the 4th Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, IPMU 92, (1992) 789-794, Palma de Mallorca, 6-10 July 92.
A definition of distinctness that underlies the use of Dempster’s rule of combination.
Distinct Evidence.ps
Distinct Evidence.pdf

Smets Ph. (1993) Belief Functions : the Disjunctive Rule of Combination and the Generalized Bayesian Theorem.
International Journal of Approximate Reasoning 9 (1993) 1-35.
A presentation of Bayes theorem within the belief function framework and the introduction of the concept of a disjunctive combination rule.
GBT & DRC.pdf

Smets Ph. (1993) Jeffrey's rule of conditioning generalized to belief functions.
Proceedings of the 9th Conference on Uncertainty in Artificial Intelligence, UAI93, Heckerman D., Mamdani A. (eds.). Morgan Kaufmann Publ., San Mateo, California. (1993) 500-505 .
Generalizing Jeffrey’s rule of conditioning.
Jeffrey rule conditioning.ps
Jeffrey rule conditioning.pdf

Smets Ph. (1997) The a-junctions : the Commutative Combination Operators applicable to Belief Functions.
Gabbay D., Kruse R., Nonnengart A. and Ohlbach H. J. (eds.) Qualtitative and quantitative practical reasoning. Springer Verlag, Berlin, (1997) 131-153.
Developing generalized weighted conjunctions, disjunctions, exclusive or etc…
Alpha-Junctions.ps
Alpha-Junctions.pdf

Smets Ph. (2004) Analyzing the Combination of Conflicting Belief Functions.
Submitted.
Survey and critial analysis of the methods propsed for handling the conflict that an appeaar when conjunctively combining two belief functions.
Combi_Confl.pdf

Smets Ph. (2005) Managing Deceitful Reports with the Transferable Belief Model.
Submitted.
Suppose a deceiver agent tampers the message send by a remote sensor to a coordination center. We analysis one strategy that could be used, and how to cope with such a possibly tampered collected message. The method is based on negated belief functions.
Deceit_Sensor.pdf

Smets Ph. (1993) Quantifying Beliefs by Belief Functions : An Axiomatic Justification.
Proceedings of the 13th International Joint Conference on Artificial Intelligence, IJCAI’93, Morgan Kaufmann Publ., San Mateo, California. (1993) 598-603.
A set of axiom that leads to the use of belief functions as the only way to quantify degrees of credibility. Short version of next paper.
Axioms IJCAI.ps
Axioms IJCAI.pdf

Smets Ph. (1995) The Axiomatic Justification of the Transferable Belief Model.
Unpublished. Only available as TR/IRIDIA/1995-8.1
The full axiomatization of the TBM with the proofs and many discussed subtleties. What is behind the 1993 and 1997 papers.
Axioms Detailed.ps
Axioms Detailed.pdf

Smets Ph. (1997) The Normative Representation of Quantified Beliefs by Belief Functions.
Artificial Intelligence 92 (1997) 229-242.
A short paper presenting the axiomatic justification of the use of belief functions for representing quantified beliefs. Some differences with Smets 1993.
Axioms AIJ.ps
Axioms AIJ.pdf

Smets Ph. (2002) Showing why measures of quantified beliefs are belief functions.
in Intelligent Systems for Information Processing: From Representation to Applications, Bouchon, B. and Foulloy, L. and Yager, R.R. (Eds.) Elsevier, Amsterdam, 2003,265-276.
Building a counter example of what happens if a mass is negative. Based on the fact that revision of beliefs can always be represented by a matrix product.
NegBelAccident.pdf

Smets Ph. (1993) Probability of Provability and Belief Functions
Proceedings of the European Conference on Symbolic and Quantitative Approaches to Reasoning and Uncertainty, ECSQARU’93, Clarke M., Kruse R., Moral S. (eds), Springer-Verlag (1993) 332-340 (short version).
Also in Logique et Analyse 133-134 (1991) 177-195 (long version).
How to get belief functions from the concept of the probability of provability and how to handle conditioning events.
Proba Deductibility.ps
Proba Deductibility.pdf

Alechina N. and Smets Ph. (1994) A Note on Modal Logics for Partial Belief.
Unpublished. Only as TR/IRIDIA/1994-25

Xu H. and Smets Ph.(1995) Generating Explanations for Evidential Reasoning.
Uncertainty in AI 95. Besnard Ph. & Hanks S. (eds), Morgan Kaufmann, San Mateo, California (1995) 574-581.
How to explain the origin of a computed beliefs, which piece of evidence is essentially responsible for the derived beliefs.

Xu H. and Smets Ph. (1996) Some Strategies for Explanations in Evidential Reasoning.
IEEE Transactions on Systems, Man & Cybernetics 26A (1996) 599-607.
Explaining the origin of a computed belief and finding which pieces of evidence are influencing the results.

Ben Yaghlane B., Smets Ph. and K. Mellouli K. (2001) Belief Function Independence: II. The Conditional Case.
International J. Approximate Reasoning, 31:31-75
Non interactivity between 2 variables given a third one under a belief function is equal to conditional irrelevance and irrelevance preservation under Dempster's rule of combination. Full version for the conditional case.
Conditional_Independence.pdf

Ben Yaghlane B., Smets Ph. and K. Mellouli K. (2001) Belief Function Independence: I. The Marginal Case.
International J. Approximate Reasoning, 29:47-70
Non interactivity between 2 variables under a belief function is equal to irrelevance and irrelevance preservation under Dempster's rule of combination. Full version for the marginal case.
Marginal_Independence.pdf

Ben Yaghlane B., Smets Ph. and K. Mellouli K. (1999) Independence and Non-Interactivity in the Transferable Belief Model.
Workshop on Conditional Independence Structures and Graphical Models. Eds F. Matus and M. Studeny, Toronto, Canada (1999) Abstract book, 4-5
Non interactivity between 2 variables under a belief function is equal to irrelevance and irrelevance preservation under Dempster's rule of combination.
IndCond-Toronto.ps
IndCond-Toronto.pdf

Ben Yaghlane B., Smets Ph. and K. Mellouli K. (2000) On Conditional Belief Function Independence.
Workshop on Partial Knowledge and Uncertainty: Independence, Conditioning, Inference, Eds R. Scozzafava and B. Vantaggi, Rome, Italy (2000).
The concept of conditional independence when uncertainty is expressed by belief functions.
condindep-Rome.ps
condindep-Rome.pdf

Ben Yaghlane B., Smets Ph. and K. Mellouli K. (2000) Independence Concepts for Belief Functions.
Proceedings 8th International Conference IPMU Information Processing and Management of Uncertainty in Knowledge-based Systems, Vol. I, pp 357-364, Madrid, Spain (2000).
Finding a common sense meaningful definition of doxastic independence. Based on the concepts of non-interactivity and irrelevance extended to belief functions.
indconcept-ipmu.ps
indconcept-ipmu.pdf

Networks and algorithms.

Xu H. and Smets Ph. (1994) Evidential Reasoning with Conditional Belief Functions.
Uncertainty in AI’94, Heckerman D., Poole D. & Lopez de Mantaras R. (eds), Morgan Kaufmann, San Mateo, California (1994) 598-606.
Algorithmic optimalization. For longer version see next paper.

Xu H. and Smets Ph. (1996) Reasoning in Evidential Networks with Conditional Belief Functions.
International Journal of Approximate Reasoning 14 (1996) 155-185.
How to propagate conditional beliefs in evidential networks, and solving some problems in order to be able to use directed graphs instead of the classical undirected graph as described initially for valuation based systems.

Smets Ph. (1978) Un modèle mathématico-statistique simulant le processus du diagnostic médical.
Thèse d'agrégation de l'Enseignement Supérieur. Presses Universitaires. 269 pages. (available through University Microfilm International, 30-32 Mortimer street, London W1N 7RA, thesis 80-70,003).
The first definition of the Generalized Bayesian Theorem. My Ph.D. thesis, in French.

Smets Ph. (1981) The Degree of Belief in a Fuzzy Event.
Information Sciences 25 (1981) 1-19.
The degree of belief in a fuzzy event as the lower expectation of the characterisric function of the fuzzy set.

Smets Ph. (1983) Information Content of an Evidence.
Int. J. Man Machine Studies, 19 (1983) 33-43.
A measure that is additive for Dempster's rule of combination, a weighted sum of the logartithms of the commonality function. Unrelated to Shannon entropy.

Smets Ph., Magrez P. (1985) Additive Structure of the Measure of Information Content,
Approximate Reasoning in Expert Systems. M.M. Gupta, A. Kandel, W. Bandler and J.B. Kiszkaed eds. North Holland, (1985) 195-197.
Showing why measures of information content should be somehow additive.

Smets Ph. (1986) Bayes' theorem generalized for belief functions.
ECAI-86,vol II (1986) 169-171.
A short version of the 1993 paper on Bayes Theorem.

Smets Ph. (1987) Belief functions and generalized Bayes theorem.
Second IFSA Congress, Tokyo, Japan (1987) 404-407.
A short version of the 1993 paper on Bayes Theorem.

Smets Ph. (1992) Resolving misunderstandings about belief functions.
International Journal of Approximate Reasoning 6 (1992) 321-344.
A response to the many criticisms raised by J. Pearl.
Resp Pearl Criticisms.ps
Resp Pearl Criticisms.pdf

Smets Ph. (1992) The nature of the unnormalized beliefs encountered in the transferable belief model.
Proceedings of the 8th Conference on Uncertainty in Artificial Intelligence, Dubois D., Wellmann M.P., D’Ambrosio B. and Smets Ph. (eds), Morgan Kaufmann Publ., San Mateo, California, (1992) 292-297.
Explaining what is m (Ø) > 0.
Meaning of m(Ø)>0.ps
Meaning of m(Ø)>0.pdf

Nguyen T. H. and Smets Ph. (1993) On Dynamics of Cautious Belief and Conditional Objects.
International Journal of Approximate Reasoning 8 (1993) 89-104.
How to justify Dempster’s rule of conditioning within the Theory of Conditional Objects.

Smets Ph. (1994) Belief induced by the Knowledge of some Probabilities.
Uncertainty in AI’94, Heckerman D., Poole D., & Lopez de Mantaras R. (eds), Morgan Kaufmann, San Mateo, California (1994) 523-530.
What is the belief induced by partial information on the value of the probabilities.
BF induced by ULP.ps
BF induced by ULP.pdf

Smets Ph. (1994) The Representation of Quantified Belief by the Transferable Belief Model.
Unpublished. only as TR/IRIDIA/1994-19.
Several new results on the TBM, but not valid for what concerns the cautious combination rule.

Smets Ph. (1995) The Canonical Decomposition of a Weighted Belief.
International Joint Conference on AI, IJCAI’95, Montréal, Canada (1995) 1896-1901.
Any belief function is in decomposable (generalized) simple support functions and a presentation of the concepts of negative beliefs (good reasons NOT to believe)
Canonical Decmposition.ps
Canonical Decmposition.pdf

Smets Ph. (2002) Matrix Calculus for Belief Functions.
Int. J. Approximate Reasoning, (2002) 31,1-30.
How to perform the belief function computation using matric calculus.
MatrixRepresentation.pdf

Smets Ph. (2004) Belief Functions on Real Numbers.
Int. J. Approx. Reasoning: Forthcoming.
Extending belief function theory on the reals.
Continuous.pdf

Smets Ph. (1978) Theory of Evidence and Medical Diagnostic.
Medical Informatics Europe 78. J. Anderson, ed. Springer Verlag, Berlin, (1978) 285-291.

Smets Ph. (1979) Modèle quantitatif du diagnostic médical.
Bulletin de l'Académie Royale de Médecine de Belgique 134 (1979) 330-343.

Smets Ph. (1979) Medical Diagnosis : Fuzzy Sets and Degree of Belief.
MIC 79. J. Willems ed, Leuven, Belgium (1979) 185-189.

Smets Ph. (1981) Medical Diagnosis : Fuzzy Sets and Degrees of Belief.
Int. J. Fuzzy Sets and systems, 5 (1981) 259-266.
Explaining that the medical diagnostic process is the assessment of the degree of belief in a fuzzy event. The diagnostic class is a fuzzy set; the clinician can only express his/her beliefs (that are represented by belief functions)

Smets Ph. (1992) The Transferable Belief Model for Expert Judgments and Reliability Problems.
Reliability Engineering and System Safety 38 (1992) 59-66.
Potential applications of the TBM in reliability problems.
Expert Judgements & Reliability.ps
Expert Judgements & Reliability.pdf

Smets Ph. (1998) The Application of the Transferable Belief Model to Diagnostic Problems.
Int. J. Intelligent Systems 13 (1998) 127-158.
A detailled presentation of the possible use of the tbm for problems of diagnostic, with an explanation on how beliefs can be asessed.
Diagnosis.ps
Diagnosis.pdf

Smets Ph. (1999)  Practical Uses of Belief Functions.
Laskey K. B. and Prade H. (eds.) Uncertainty in Artificial Intelligence 15. UAI99 (1999) 612-621
Presenting four real applications where belief functions provide convenient tools and where a probability approach might encountered serious difficulties.
Practical Uses.ps
Practical Uses.pdf

Ayoun, A. and Smets, Ph. (2001) Data association in multi-target detection using the transferable belief model.
Intern. J. Intell. Systems, 16:1167-1182.
How to associate sensors and sources using the mass given to the empty set, i.e., the measure of conflict as described in the TBM.
Submarine.ps
Submarine.pdf

Dubois, D., Grabisch, M., Prade, H. and Smets, Ph. (2001) Using the transferable belief model and a qualitative possibility theory approach on an illustrative example: the assessment of the value of a candidate.
Intern. J. Intell. Systems, 16:1245-1272.
How to use the TBM and the qualitative possibility theory in a practical application dealing with expert opinion pooling. Computation fully detailled.
SelCandiFusion.ps
SelCandiFusion.pdf

Delmotte, F. and Smets, Ph. (2001) Target Identification Based on the Transferable Belief Model Interpretation of Dempster-Shafer Model. Pars I: Methodology. Pars 2: Application.
IRIDIA Technical Report
The use of the TBM for identification problems in the framework of multi-sensor data fusion. Explaining the general Bayesian Theorem and the pignistic transformation. It shows also its better computational efficiency when compared with the classical probability method. This is the full version of the same paper published by IEE-SMC.
TargetIdentif-1.pdf
TargetIdentif-2.pdf

Delmotte, F. and Smets, Ph. (2004) Target Identification Based on the Transferable Belief Model Interpretation of Dempster-Shafer Model.
IEEE Trans. Syst., Man, Cybern. A:34, 457-471, (2004)
See previous TR. This a published but shorter version.
gbt_targetid_IEEE.pdf

Ristic, B. and Smets, Ph. (2004) Target identification using belief functions and implication rules.
submitted
Combining uncertain data and rules.
identif_rule.pdf

Ristic, B. and Smets, Ph. (2004) Recursive Classification of Multiple Objects Using Discordant and Non-Specific Data.
submitted
How to build a pairwise association of targets using the mass given to the empty set, i.e., the measure of conflict as described in the TBM.
association.pdf

Ristic, B. and Smets, Ph. (2004) Kalman filters for tracking and classification and the transferable belief model.
IF04-0046, FUSION04 (2004).
The Kalman filter defined within the TBM and its use for classiccaition purpose.
kalman_class.pdf

Ristic, B. and Smets, Ph. (2004) Belief function theory on the continuous space with an application to model based classification.
ipmu04, 1119-1126.
Belief functions on the continuum and classification results that strongly differ from the Bayesian results.
cont_class.pdf

Papers on the TBM and Non-Monotonic Reasoning.

Hsia Y.-T. and Smets Ph. (1990) Belief Functions and Non-Monotonic Reasoning.
IRIDIA/TR/1990/3
A preliminary investigation for the use of belief functions in default reasoning.

Smets Ph. and Hsia Yen-Teh (1990) Defeasible Reasoning with Belief Functions.
(complement of TR/IRIDIA/90-9). Unpublished.
Further results about the use of belief functions in default reasoning.

Smets Ph., and Hsia Y.-T.(1991) Default Reasoning and the Transferable Belief Model
Uncertainty in Artificial Intelligence 6, P.P. Bonissone, M. Henrion, L.N. Kanal, J.F. Lemmer (Editors), Elsevier Science Publishers, (1991) 495-504.
Some solutions for default reasoning (the Tweety problem).
NMR & TBM.pdf

Benferhat S., Saffiotti A. and Smets Ph.(1995) Belief Functions & Default Reasoning
Proceedings of the 11th Conference on Uncertainty in AI 95, Besnard Ph. and Hanks S. (eds), Morgan Kaufmann Publ., San Mateo, California (1995) : 19-26.
The introduction of the e-belief functions (which values are infinitely close to 0 and 1) and their use for solving problems of default reasoning. Short Version.
Epsilon bel fct UAI.ps
Epsilon bel fct UAI.pdf

Benferhat S., Saffiotti A. and Smets Ph.(2000) Belief Functions and Default Reasoning.
Artifical Intelligence, (2000) 122: 1-69.
Solving default reasoning problems with belief functions which values are infinitesimaly close to 0's and 1's. This approach can be particularized into the models proposed today. A new approach is also developed that seems to satisfy all 'natural' requirements.
Epsilon_bel_fct_UAI.ps
Epsilon_bel_fct_UAI.pdf

Smets Ph. (2005) Decision Making in the TBM: the Necessity of the Pignistic Transformation.
Int. J. Approximate Reasoning, 38, 133-147 (2005).
Proving the pignistic transformation is compulsory.
nec_pigt.pdf

Smets Ph. (2002) Decision Making in a Context where Uncertainty is Represented by Belief Functions.
Belief Functions in Business Decisions. Srivastava R. and Mock, T.J. (ed.) Physica-Verlag, Heidelberg, Germany (2002) 17-61.
Survey of decision making within the upper-lower probability and the TBM frameworks.
DM-BF.ps
DM-BF.pdf

Smets Ph. (1990) Constructing the pignistic probability function in a context of uncertainty.
Uncertainty in Artificial Intelligence 5, M. Henrion, R.D. Shachter, L.N. Kanal, and J.F. Lemmer (Editors), Elsevier Science Publishers (1990) 29-39.
Presenting and justifiying by rationality requirements the transformation between belief functions and probability functions when decision must be made.
Pignistic Transformation.ps
Pignistic Transformation.pdf

Xu Hong, Hsia Yen-The and Smets Ph.(1993) A Belief-Function Based Decision Support System.
Proceedings of the 9th Conference on Uncertainty in AI 93, Heckerman D., Mamdani A. (eds), Morgan Kaufmann Publ.,San Mateo, California (1993) 535-542.
Applying the TBM to a problem of decision making and building the optimal strategy in detecting the origin of some radioactivity leakage.

Smets Ph.(1993) No Dutch Book can be built against the TBM even though update is not obtained by Bayes rule of conditioning.
SIS, Workshop on Probabilistic Expert Systems. R. Scozzafava (ed.), Roma, Italy (1993) 181-204.
Solving the decision making problem with belief functions in dynamic decisions making.
Dynamic Dutch Books.ps
Dynamic Dutch Books.pdf

Xu H., Hsia Y.-T. and Smets Ph.(1996) The Transferable Belief Model for Decision Making in the Valuation-Based Systems.
IEEE Transactions on Systems, Man, and Cybernetics, 26A (1996) 698-707.
Presenting the software that can both compute beliefs and make decisions using the pignistic probabilities and optimalizing the expected utilities.

Elouedi Z., Mellouli K. and Smets Ph. (2004) Assessing sensor reliability for multisensor data fusion with the transferable belief model.
IEEE Trans. SMC B:34,782-787 (2004)
Evaluating the reliability of a sensor in a classification task when the uncertainty is represented by belief functions as understood in the TBM.
tuning_rel.pdf

Elouedi Z., Mellouli K. and Smets Ph. (2002) The Evaluation of Sensors' Reliability and their Tuning for Multisensor Data Fusion within the Transferable Belief Model.
in Benferhat, S. and Besnard, P. Symbolic and Quantitative Approaches to Reasoning with Uncertainty. ECSQARU 2001. Springer-Verlag, Berlin, 2001, pages 350-361
Short version of previous paper.
Tuning_bf.pdf

Elouedi Z., Mellouli K. and Smets Ph. (2002) A Pre-Pruning Method in Belief Decision Trees.
IPMU 2002, Annecy, France, 579-586.
A pre-pruning method to reduce the complexity of belief decision trees.
BDT_PrePruning.pdf

Elouedi Z., Mellouli K. and Smets Ph. (2000) Decision trees using belief function theory.
Proceedings eighth International Conference IPMU: Information Processing and Management of Uncertainty in Knowledge-based Systems, Madrid (2000) Volume I, 141-148.
Building and using belief decision trees, a generalization od ID3, based on the averaging approach, when classes in the training set are known up to a belief function of the set of possible classes. Its use when attributes of the new cases are knonw as disjunctions of possible values.
bdt-ipmu00.ps
bdt-ipmu00.pdf

Elouedi Z., Mellouli K. and Smets Ph. (2000) Classification with Belief Decision Trees.
Proceedings of the 9th International Conference on Artificial Intelligence : Methodology, Systems, Architectures. AIMSA 2000, Varna, Bulgaria. Springer Lecture Notes of Artificial Intelligence (2000).
Building and using belief decision trees, a generalization of ID3, based on the averaging approach, when classes in the training set are known up to a belief function of the set of possible classes. Its use when user has only belief functions about what are the values of some attributes of the new cases.
bdt-aimsa00.ps
bdt-aimsa00.pdf

Elouedi Z., Mellouli K. and Smets Ph. (2001) Belief Decision Trees: Theoretical Foundations.
Int. J. Approximate Reasoning, 28:91-124.
Full paper presenting the Belief Decision Trees, a generalization of ID3. Knowledge about the classes of the data in the training set representeed by a belief function. Knowledge about the values of the attributes for new cases representeed by a belief function. Two approaches: the averaging and the conjunctive approaches.
BelDecTreeTheory.ps
BelDecTreeTheory.pdf

Papers on the FMT (Fast Möbius Transform).

Kennes R. and Smets Ph. (1990) Fast algorithms for Dempster-Shafer theory.
Uncertainty in Knowledge Bases, B. Bouchon-Meunier, R.R. Yager, L.A. Zadeh (Editors), Lecture Notes in Computer Science 521, Springer-Verlag, Berlin (1991) 14-23.
Full paper in Kennes, 1992
An optimal computational solution for the algorithmic transformations between belief functions and basic belief assignments and conversely.

Kennes R. and Smets Ph. (1991) Computational Aspects of the Möbius Transformation.
Uncertainty in Artificial Intelligence 6, P.P. Bonissone, M. Henrion, L.N. Kanal, J.F. Lemmer (Editors), Elsevier Science Publishers (1991) 401-416.
Full paper in Kennes, 1992
An optimal computational solution for the algorithmic transformations between commonality functions and basic belief assignments and conversely. And also an application to Dempster’s combination rule.

Kennes R.(1992) Computational Aspects of the Möbius Transformation of Graphs.
IEEE Trans. SMC. 22 (1992) 201-223.
The full paper on the Fast Möbius transform. It presents an optimal computational solution for the transformation between belief functions, plausibility functions, commonality functions and basic belief assignments.

Smets Ph. (1987) Upper and lower probability functions versus belief functions.
Proc. International Symposium on Fuzzy Systems and Knowledge Engineering, Guangzhou, China (1987) 17-21.

Smets Ph. (1988) Belief functions versus probability functions.
Bouchon B., Saitta L. and Yager R. Uncertainty and Intelligent Systems. Springer Verlag, Berlin (1988) 17-24

Smets Ph. (1988) Transferable belief model versus Bayesian model.
Kodratoff Y. (ed.) ECAI 1988, Pitman, London (1988) 495-500.

Smets Ph. (1990) The transferable belief model and possibility theory
Proc. NAFIPS-90, (1990) 215-218.
State of belief can be equated to the knowledge generated by a fuzzy event.
TBM & Possibility Th.ps
TBM & Possibility Th.pdf

Smets Ph. (1991) The Transferable Belief Model and other Interpretations of Dempster-Shafer's Model.
Uncertainty in Artificial Intelligence 6, P.P. Bonissone, M. Henrion, L.N. Kanal, J.F. Lemmer (Editors), Elsevier Science Publishers (1991) 375-383.
See Smets (1994) for a much longer version.
Discussions about the many interpretations given to Dempster-Shafer theory.
TBM & DST.ps
TBM & DST.pdf

Smets Ph. (1992) The Transferable Belief Model and Random Sets.
International Journal of Intelligent Systems 7 (1992) 37-46.
Distinguising between the TBM and the random set interpretation of Dempster-Shafer theory.
TBM-RandSet.ps
TBM-RandSet.pdf

Smets Ph.(1994) What is Dempster-Shafer's model ?
Advances in the Dempster-Shafer Theory of Evidence, Yager R.R., Fedrizzi M. and Kacprzyk J.(eds.), Wiley (1994) 5-34.
A full comparison of the many interpretations of Dempster-Shafer’models.
What is DS.ps
What is DS.pdf

Smets Ph.(2000) Quantitative Epistemic Possibility Theory seens as an Hyper Cautious Transferable Belif Model.
LFA La Rochelle, TR/IRIDIA-2000-18
Providing a semantic to the values given to the degrees of subjective possibility. Based on the TBM and cautious combination rules.
Possib_Semantic.ps
Possib_Semantic.pdf

Dubois D., Prade H. and Smets Ph. (2001) New Semantics for Quantitative Possibility Theory.
ISIPTA'01. Ithaca, NY.
Semantic for both the subjective and objective possibility measures.
SemanticPossSubjObj.pdf

Cooke R. and Smets Ph. (2000) Self conditioning probabilities and probabilistic interpretations of belief functions.
TR/IRIDIA-2000:19, submitted for publication
A purely probabilistic way to produce basi belief masses, and its links with Dempster's model and the model for probabilities given to modal propositions.
Self_Conditioning.ps
Self_Conditioning.pdf

Smets Ph. (1991) Varieties of ignorance
Information Sciences 57-58 (1991) 135-144.
An overview about the forms of uncertainties.
VarietyIgnorance.ps
VarietyIgnorance.pdf

Dubois D., Garbolino P., Kyburg H.E., Prade H. and Smets Ph. (1991) Quantified Uncertainty.
J. Applied Non-Classical Logics 1 (1991) 105-197.
A set of ten critical questions are discussed at length by advocates of probability, upper and lower probability, possibility, and belief functions.

Dubois D., Prade H. and Smets Ph.(1994) Partial Truth is not Uncertainty: Fuzzy Logic versus Possibilistic Logic.
IEEE Expert vol. 9.4 (1994) 15-19.
A response to a criticism of fuzzy logic based on erroneous assumptions, but widely published.
Gradual_vs_Uncert.ps
Gradual_vs_Uncert.pdf

Smets Ph.(1995) Non Standard Probabilistic and Non Probabilistic Representations of Uncertainty.
IPMU'94, Bouchon Meunier B., Yager R.R., Zadeh L. eds, LNCS945. Springer-Verlag, Heidelberg, (1995) 13-40.
Also in Advances in Fuzzy Sets Theory & Technology Wang P.P. ed.Vol. III, Duke University, Durham, NC, (1995) 125-154.
Distinguishing the various theories built to represent uncertainty.
Non St Pr - NonPr.ps
Non St Pr - NonPr.pdf

Smets Ph. (1995) Probability, Possibility, Belief : which for what ?
Foundations and Applications of Possibility Theory De Cooman G., Ruan D., Kerre E.E. eds, World Scientific, Singapore (1995) 20-40.
Updated and full version in Smets 1998, see below in Handbook of Defeasible Reasoning…
Discussing the applicability of the various models.

Dubois D., Prade H. and Smets Ph.(1996) Representing partial ignorance.
IEEE System Machine and Cybernetic 26 (1996) 361-377.
A general discussion comparing the probability, belief and possibilistic solutions.
Rep Partial Ignorance.ps
Rep Partial Ignorance.pdf

Smets Ph.(1997) Imperfect information : Imprecision - Uncertainty.
Uncertainty Management in Information Systems. From Needs to Solutions. A. Motro and Ph. Smets (eds.), Kluwer Academic Publishers (1997) 225-254.
A long presentation comparing the model for representing imprecision and uncertainty.
Imperfect Data.ps
Imperfect Data.pdf

Smets Ph.(199x) Theories of Uncertainty.
Handbook for Fuzzy Computation.
Another survey of the concept of uncertainty and its representation.
Uncertainty HbkFuzzyComput.ps
Uncertainty HbkFuzzyComput.pdf

Smets Ph.(1998) Numerical Representation of Uncertainty.
Handbook of Defeasible Reasoning and Uncertainty Management Systems. Gabbay D. and Smets Ph. (Series Eds). Dubois D. and Prade H. (Vol. Eds.) Vol. 3: Belief Change. Kluwer, Doordrecht (1998) 265-309.
Discussing the various models and their behavior when beliefs change from factual or generic revision. Explain the difference between these forms of belief revision.
Num Repr Unc.ps
Num Repr Unc.pdf

Smets Ph.(1998) Probability, Possibility, Belief: Which and Where ?
Handbook of Defeasible Reasoning and Uncertainty Management Systems. Gabbay D. and Smets Ph. (Series Eds). Ph. Smets (Vol. eds.), Vol. 1 : Quantified Representation of Uncertainty & Imprecision, Kluwer, Doordrecht (1998) 1-24.
A up-to-date survey of the various theories proposed for the representation of quantified beliefs.
Prob Poss Bel.ps
Prob Poss Bel.pdf

Dubois, D. and Prade, H. and Smets, Ph.(2003) A definition of subjective possibility.
Operations Research and Decisions (2003) 4:7-22.
defsubjposs.pdf

Smets Ph. (1982) Probability of a Fuzzy Event : an Axiomatic Approach.
Int. J. Fuzzy Sets and systems, 7 (1982) 153-164.

Smets Ph. (1982) Elementary Semantic Operators.
Fuzzy Set and Possibility theory. R. Yager ed. Pergamon Press, New York (1982) 247-256.

Smets Ph. (1982) Possibilistic Inference from Statistical Data.
Second World Conference on Mathematics at the Service of Man. A. Ballester, D. Cardus and E. Trillas eds. Universidad Politecnica de Las Palmas, Spain (1982) 611-613.
Showing that possibility measures are analogous to likelihood functions.

Smets Ph. (1982) Subjective Probability and fuzzy Measures.
Fuzzy Information and Decision Processes. M. Gupta and E. Sanchez eds. North Holland, (1982) 87-91.

Smets Ph. (1983) Fuzzy Sets Theory for Medical Decision Making.
Objective Medical Decision-Making; System Approach in Acute Disease. J.E.W. Beneken and S.M. Lavelle eds.Springer Verlag, Berlin (1983) 7-19.

Smets Ph. (1985) Probability of a Fuzzy Event.
Systems and Control Encyclopedia. M. G. Singh ed. Pergamon, Oxford, GB. (1985) 1802-1805.

Smets Ph., Magrez P. (1987) Implication in Fuzzy Logic.
Int. J. Approximate Reasoning 1 (1987) 327-348.

Smets Ph., Magrez P. (1988) The Measure of the Degree of Truth and of the Grade of Membership.
Int. J. Fuzzy Sets and Systems. 25 (1988) 67-72.

Magrez P. and Smets Ph. (1989) Epistemic necessity, possibility and truth. Tools for dealing with imprecision and uncertainty in fuzzy knowledgebased systems.
Int.J.Approximate Reasoning. 3 (1989) 35-57.

Magrez P. and Smets Ph. (1989) Fuzzy modus ponens: a new model suitable for applications in knowledge-based systems.
Int.J.Intelligent Systems 4 (1989) 181-200. (Reprinted in Dubois D., Prade H. and Yager R.R. Readings in Fuzzy Sets for Intelligent Systems. Morgan Kaufman, San Mateo, California (1993) 565-574)

Smets Ph. (1991) Implication and modus ponens in fuzzy logic.
Goodman I.R., Gupta M.M., Nguyen H.T. and Rogers G.S. Conditional logic in expert systems. Elsevier, Amsterdam (1991) 235-268.
A synthese of the four previous papers by Magrez and Smets.

Berenji H., Bonissone P., Bezdek J., Dubois D., Kruse R., Prade H., Smets Ph. and Yager R. (1994) A reply to the Paradoxical Success of Fuzzy Logic. AI Magazine, 15 (1994) 6-8.
A reply to the 'empty' paper of Elkan. Elkan introduces an inadequate axiom under which fuzzy logic degenerates into binary logic. That property was known for long, and the inadequacy of the axiom was well known.
Details in Dubois D., Prade H. and Smets Ph.(1994) IEEE Expert vol. 9.4, (1994) 15-19.
Elkan_reply.ps
Elkan_reply.pdf